scholarly journals The influence of stratification upon small-scale convectively-driven dynamos

2010 ◽  
Vol 6 (S271) ◽  
pp. 197-204 ◽  
Author(s):  
Paul J. Bushby ◽  
Michael R. E. Proctor ◽  
Nigel O. Weiss
Keyword(s):  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Small Scale ◽  
Initial Growth ◽  
Dynamo Action ◽  
Quiet Sun ◽  
Electrically Conducting ◽  
Solar Observations ◽  
Electrically Conducting Fluid ◽  
Convective Motions

AbstractIn the quiet Sun, convective motions form a characteristic granular pattern, with broad upflows enclosed by a network of narrow downflows. Magnetic fields tend to accumulate in the intergranular lanes, forming localised flux concentrations. One of the most plausible explanations for the appearance of these quiet Sun magnetic features is that they are generated and maintained by dynamo action resulting from the local convective motions at the surface of the Sun. Motivated by this idea, we describe high resolution numerical simulations of nonlinear dynamo action in a (fully) compressible, non-rotating layer of electrically-conducting fluid. The dynamo properties depend crucially upon various aspects of the fluid. For example, the magnetic Reynolds number (Rm) determines the initial growth rate of the magnetic energy, as well as the final saturation level of the dynamo in the nonlinear regime. We focus particularly upon the ways in which the Rm-dependence of the dynamo is influenced by the level of stratification within the domain. Our results can be related, in a qualitative sense, to solar observations.

scholarly journals Small-scale dynamo action in rotating compressible convection

2011 ◽  
Vol 690 ◽  
pp. 262-287 ◽  
Author(s):  
B. Favier ◽  
P. J. Bushby
Keyword(s):  
Reynolds Number ◽  
Energy Density ◽  
Thermal Stratification ◽  
Magnetic Energy ◽  
Critical Value ◽  
Magnetic Reynolds Number ◽  
Small Scale ◽  
Dynamo Action ◽  
Lower Bounding ◽  
The Mean

AbstractWe study dynamo action in a convective layer of electrically conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly conducting boundary conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number ${R}_{M} $ that is based upon the horizontal integral scale and the horizontally averaged velocity at the mid-layer of the domain, we find that rotation tends to reduce the critical value of ${R}_{M} $ above which dynamo action is observed. Increasing the level of thermal stratification within the layer does not significantly alter the critical value of ${R}_{M} $ in the rotating calculations, but it does lead to a reduction in this critical value in the non-rotating cases. At the highest computationally accessible values of the magnetic Reynolds number, the saturation levels of the dynamo are similar in all cases, with the mean magnetic energy density somewhere between 4 and 9 % of the mean kinetic energy density. To gain further insights into the differences between rotating and non-rotating convection, we quantify the stretching properties of each flow by measuring Lyapunov exponents. Away from the boundaries, the rate of stretching due to the flow is much less dependent upon depth in the rotating cases than it is in the corresponding non-rotating calculations. It is also shown that the effects of rotation significantly reduce the magnetic energy dissipation in the lower part of the layer. We also investigate certain aspects of the saturation mechanism of the dynamo.

scholarly journals Optimal dynamo action by steady flows confined to a cube

2015 ◽  
Vol 783 ◽  
pp. 23-45 ◽  
Author(s):  
L. Chen ◽  
W. Herreman ◽  
A. Jackson
Keyword(s):  
Incompressible Flows ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Steady Flows ◽  
Dynamo Action ◽  
Electrically Conducting ◽  
Energy Growth ◽  
Optimal Flow ◽  
Complementary Set ◽  
The Magnetic Field

Many flows of electrically conducting fluids can spontaneously generate magnetic fields through the process of dynamo action, but when does a flow produce a better dynamo than another one or when is it simply the most efficient dynamo? Using a variational approach close to that of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find optimal kinematic dynamos within a huge class of stationary and incompressible flows that are confined in a cube. We demand that the magnetic field satisfies either superconducting (T) or pseudovacuum (N) boundary conditions on opposite pairs of walls of the cube, which results in four different combinations. For each of these set-ups, we find the optimal flow and its corresponding magnetic eigenmodes. Numerically, it is observed that swapping the magnetic boundary from T to N leaves the magnetic energy growth nearly unchanged, and both $+\boldsymbol{U}$ and $-\boldsymbol{U}$ are optimal flows for these different but complementary set-ups. This can be related to work by Favier & Proctor (Phys. Rev. E, vol. 88, 2013, 031001). We provide minimal lower bounds for dynamo action and find that no dynamo is possible below an enstrophy (or shear) based magnetic Reynolds number $Rm_{c,min}=7.52{\rm\pi}^{2}$, which is a factor of $16$ above the Proctor/Backus bound.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

Spatial variations of magnetic permeability as a source of dynamo action

2013 ◽  
Vol 727 ◽  
pp. 161-190 ◽  
Author(s):  
B. Gallet ◽  
F. Pétrélis ◽  
S. Fauve
Keyword(s):  
Electrical Conductivity ◽  
Asymptotic Expansion ◽  
Magnetic Permeability ◽  
Spatial Variations ◽  
Parallel Flow ◽  
Conducting Fluid ◽  
Dynamo Action ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Spatially Varying

AbstractWe investigate dynamo action for a parallel flow of an electrically conducting fluid located over a boundary with spatially varying magnetic permeability. We first compute the dynamo threshold numerically. Then we perform an asymptotic expansion in the limit of small permeability modulation, which gives accurate results even for moderate modulation. We present in detail the mechanism at work for this dynamo. It is an interplay between shear (an $\omega $-effect) and a new conversion mechanism that originates from the non-uniform magnetic boundary. We illustrate how a similar mechanism leads to dynamo action in the case of spatially modulated electrical conductivity, a problem studied by Busse & Wicht (Geophys. Astrophys. Fluid Dyn., vol. 64, 1992, pp. 135–144). Finally, we discuss the relevance of this effect to experimental dynamos and present ways to increase the dynamo efficiency and reduce the instability threshold.

Experimental investigation of dynamo effect in the secondary pumps of the fast breeder reactor Superphenix

2000 ◽  
Vol 403 ◽  
pp. 263-276 ◽  
Author(s):  
A. ALEMANY ◽  
Ph. MARTY ◽  
F. PLUNIAN ◽  
J. SOTO
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Magnetic Energy ◽  
Experimental Studies ◽  
Phenomenological Approach ◽  
Magnetic Reynolds Number ◽  
Experimental Investigations ◽  
Dynamo Action ◽  
Experimental Conditions ◽  
Dynamo Effect

The fast breeder reactors (FBR) BN600 (Russia) and Phenix (France) have been the subject of several experimental studies aimed at the observation of dynamo action. Though no dynamo effect has been identified, the possibility was raised for the FBR Superphenix (France) which has an electric power twice that of BN600 and five times larger than Phenix. We present the results of a series of experimental investigations on the secondary pumps of Superphenix. The helical sodium flow inside one pump corresponds to a maximum magnetic Reynolds number (Rm) of 25 in the experimental conditions (low temperature). The magnetic field was recorded in the vicinity of the pumps and no dynamo action has been identified. An estimate of the critical flow rate necessary to reach dynamo action has been found, showing that the pumps are far from producing dynamo action. The magnetic energy spectrum was also recorded and analysed. It is of the form k−11/3, suggesting the existence of a large-scale magnetic field. Following Moffatt (1978), this spectrum slope is also justified by a phenomenological approach.

On kinematic dynamos

1970 ◽  
Vol 316 (1525) ◽  
pp. 153-167 ◽  
Keyword(s):  
Magnetic Field ◽  
Flow Pattern ◽  
Physical Characteristic ◽  
Major Change ◽  
Three Dimensions ◽  
Dynamo Action ◽  
Electrically Conducting ◽  
The Core ◽  
Electrically Conducting Fluid ◽  
Two Component

The method developed by Bullard & Gellman, to test flows of electrically conducting fluid in a sphere for dynamo action, is applied further to the two-component T 1 S 2c 2 flow pattern they proposed. In agreement with Gibson & Roberts, it is found that the results of the test are negative, which substantiates the indication from Braginskii’s work that the T 1 S 2c 2 flow pattern has too great a symmetry for it to act as a dynamo. However, the addition of a third component, S 2s 2 , to the flow pattern reduces the symmetry and produces results which indicate strongly that the three-component T 1 S 2c 2 S 2s 2 flow does act as a dynamo. Harmonics of magnetic field up to degree six have been taken into account, and this level of truncation appears to be justified. The streamlines of the T 1 S 2c 2 S 2s 2 flow form a distinctive whirling pattern in three dimensions, and this may be a physical characteristic necessary for dynamo action. The main magnetic fields of the T 1 S 2c 2 S 2s 2 dynamo are all toroidal, and the possibility is established that the geomagnetic dynamo is similar, with the dominant components of field being completely contained within the core. Variation of the subsidiary poloidal components of the field may then produce secular variation and even dipole reversals, without major change in the series of interactions between the toroidal components that form the basic dynamo.

scholarly journals Magnetic power spectrum in the undisturbed solar photosphere

2020 ◽  
Vol 1 (1) ◽  
pp. 1-5
Author(s):  
Valentina Abramenko ◽  
Olga Kutsenko
Keyword(s):  
Power Spectrum ◽  
Power Spectra ◽  
Active Regions ◽  
Reliable Estimate ◽  
Small Scale ◽  
Solar Photosphere ◽  
Dynamo Action ◽  
Quiet Sun ◽  
Turbulent Dynamo ◽  
Wide Range

Using the magnetic field data obtained with the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), an investigation of magnetic power spectra in the undisturbed solar photosphere was performed. The results are as follows. 1) To get a reliable estimate of a magnetic power spectrum from the uniformly distributed quiet-sun magnetic flux, a sample pattern of no less than 300 pixels length should be adopted. With smaller patterns, energy on all observable scales might be overestimated. 2) For patterns of different magnetic intensity (e.g., a coronal hole, a quiet-sun area, an area of supergranulation), the magnetic power spectra in a range of (2.5-10) Mm exhibit very close spectral indices of about -1. The observed spectrum is more shallow than the Kolmogorov-type spectrum (with a slope of -5/3) and it differs from steep spectra of active regions. Such a shallow spectrum cannot be explained by the only direct Kolmogorov’s cascade, but it can imply a small-scale turbulent dynamo action in a wide range of scales: from tens of megameters down to at least 2.5 Mm. On smaller scales, the HMI/SDO data do not allow us to reliably derive the shape of the spectrum. 3) Data make it possible to conclude that a uniform mechanism of the small-scale turbulent dynamo is at work all over the solar surface outside active regions.

On the relation between viscoelastic and magnetohydrodynamic flows and their instabilities

2003 ◽  
Vol 476 ◽  
pp. 389-409 ◽  
Author(s):  
GORDON I. OGILVIE ◽  
MICHAEL R. E. PROCTOR
Keyword(s):  
Viscoelastic Medium ◽  
Magnetic Reynolds Number ◽  
Deborah Number ◽  
Elastic Instability ◽  
Magnetorotational Instability ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Magnetohydrodynamic Flows ◽  
Elastic Instabilities ◽  
The Stability

We demonstrate a close analogy between a viscoelastic medium and an electrically conducting fluid containing a magnetic field. Specifically, the dynamics of the Oldroyd-B fluid in the limit of large Deborah number corresponds to that of a magnetohydrodynamic (MHD) fluid in the limit of large magnetic Reynolds number. As a definite example of this analogy, we compare the stability properties of differentially rotating viscoelastic and MHD flows. We show that there is an instability of the Oldroyd-B fluid that is physically distinct from both the inertial and elastic instabilities described previously in the literature, but is directly equivalent to the magnetorotational instability in MHD. It occurs even when the specific angular momentum increases outwards, provided that the angular velocity decreases outwards; it derives from the kinetic energy of the shear flow and does not depend on the curvature of the streamlines. However, we argue that the elastic instability of viscoelastic Couette flow has no direct equivalent in MHD.

scholarly journals Coronal influence on dynamos

2013 ◽  
Vol 9 (S302) ◽  
pp. 134-137 ◽  
Author(s):  
Jörn Warnecke ◽  
Axel Brandenburg
Keyword(s):  
Reynolds Number ◽  
Convection Zone ◽  
Magnetic Energy ◽  
Lower Layer ◽  
Solar Radius ◽  
Magnetic Reynolds Number ◽  
Layer Model ◽  
Dynamo Action ◽  
Turbulent Dynamo ◽  
Two Layer Model

AbstractWe report on turbulent dynamo simulations in a spherical wedge with an outer coronal layer. We apply a two-layer model where the lower layer represents the convection zone and the upper layer the solar corona. This setup is used to study the coronal influence on the dynamo action beneath the surface. Increasing the radial coronal extent gradually to three times the solar radius and changing the magnetic Reynolds number, we find that dynamo action benefits from the additional coronal extent in terms of higher magnetic energy in the saturated stage. The flux of magnetic helicity can play an important role in this context.

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